Technique of reducing the Kerr effect and extending the dynamic range in a brillouin fiber optic gyroscope

ABSTRACT

A Brillouin fiber optic gyroscope includes an intensity modulator in the optical loop which periodically attenuates the Brillouin light waves counterpropagating in the optical loop so that the counterpropagating Brillouin waves each propagate as square waves. The use of square wave modulation for the counterpropagating light wave reduces the cross-effect of the Brillouin waves to substantially the same magnitude as the self-effect so that the non-reciprocal Kerr effect is substantially reduced or eliminated. In order to support the counterpropagating square waves, the optical loop is pumped with pump light having frequency components selected to pump the optical fiber to provide Brillouin light at frequencies necessary to generate square waves in the counterpropagating Brillouin light waves. In addition, the Brillouin light must be generated at the correct intensity and phase relationship to form the square wave. Because the relationship between the pump light and the generated Brillouin light is a non-linear function, the relative magnitudes of the frequency components of the pump light are selected to be different from the relative magnitudes of the Brillouin light so that when the pump light is applied to the optical loop, the transfer function results in the correct magnitudes for the frequency components of the Brillouin light. The intensity modulator assures that the Brillouin light is maintained in the proper phase relationship to maintain a square waveform.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to Brillouin Fiber OpticGyroscopes, and more particularly to an apparatus and method forreducing the Kerr effect and extending the dynamic range of a BrillouinFiber Optic Gyroscope.

2. Description of the Prior Art

Stimulated Brillouin scattering is a non-linear process that can occurin optical fibers as a parametric interaction among a pump wave, aBrillouin wave and an acoustic wave. When the pump wave and theBrillouin wave propagate in an optical fiber, they generate an acousticwave through the process of electrostriction, which in turn causes aperiodic modulation of the refractive index. This index grating scattersthe pump light through Bragg diffraction. The scattered light is shiftedin frequency because of the Doppler shift associated with a gratingmoving at the acoustic velocity. When the Brillouin wave is propagatingin the opposite direction to the pump wave, and the frequency of theBrillouin wave is lower than the pump wave by the amount equal to theDoppler shift, the scattered light from the pump wave addsconstructively to the Brillouin wave. As a result, the Brillouin wave isamplified while the pump wave is attenuated. The frequency differenceand the gain bandwidth of this process are determined by the wavelengthof the light and material parameters of the fiber. For a wavelength of1.3 μm in a silica-based single mode fiber, for example, the frequencydifference between the pump wave and the Brillouin wave is about 13 GHzand the gain bandwidth is about 40 MHz.

Such a phenomenon has been utilized to provide for bidirectional laseroscillations in a Brillouin Fiber Optic Gyroscope (BFOG). As describedand claimed in U.S. Pat. No. 4,530,097, entitled "Brillouin Ring Laser",assigned to the assignee of the present invention, a BFOG comprises alaser source which provides pump light into a fiber. U.S. Pat. No.4,530,097 is incorporated herein by reference. A directional couplersplits the pump light traveling into a resonator into two portions, onetraveling in the clockwise (CW) direction and the other in thecounterclockwise (CCW) direction. The length of the resonator isadjusted so that the pump frequency matches one of the longitudinalmodes in the resonator. When the pump power exceeds the threshold levelfor Brillouin oscillation, Brillouin waves will start propagating,resulting in bidirectional laser oscillations. The CW and CCW Brillouinlight waves are combined to produce an interference signal. Once thegyroscope rotates, the resonant frequencies of the CW and CCW Brillouinlaser oscillations separate, and the interference signal produces abeat-frequency which is proportional to the rotation rate of thegyroscope.

There are inherent problems with existing BFOG technology that preventsprecise measurement of this rotation rate. One such problem is thebeat-frequency offset and its non-linear response resulting from theKerr effect.

The Kerr effect is a phenomenon that occurs when the refractive index ofa fiber seen by a Brillouin signal is slightly modified by the signal'sown intensity, as well as other light intensities circulating within theresonant cavity of the BFOG. When the circulating intensities of the CWand CCW Brillouin signals are unequal, there is a net imbalance of theoptical path length of the cavity seen by these two waves. Thisimbalance of the Brillouin intensities of the optical path lengthtranslates to a beat-frequency offset. In addition, when the imbalanceof the Brillouin intensities is not constant as the rotation ratechanges, a non-linear scale factor results.

There are two causes for the imbalance of the Brillouin intensities. Oneis a result of imbalance of the pump intensities themselves. The pumplights are circulating bidirectionally inside the resonator, and the CWpump provides gain for the CCW Brillouin signal while the CCW pumpprovides gain for the CW Brillouin signal. Any imbalance of the CW andCCW pump intensities thus results in the imbalance of the Brillouinintensities. Existing BFOG technology utilizes a Y-branch beam splitteror an optical coupler to provide an approximate fifty-fifty power splitfrom a single source. Imperfections in manufacture of the splitter orcoupler generally result in an imbalance of the Brillouin intensitiesobtained from such a split. Unequal loss in the fiber arms connectingthe Y-branch or the coupler to the fiber ring resonator also results inan imbalance of the Brillouin intensities. This imbalance of Brillouinintensities in turn results in the scale factor offset through the Kerreffect.

The second cause of imbalance is due to the "resonant walk-off effect."When the resonant cavity loop is at rest, both pump waves will have afrequency at a resonant frequency of the cavity. Upon rotation of theloop, each of the counter-propagating pump waves will have a differentoptical path length around the loop, due to the Sagnac effect. The pathlength for one of the waves increases, while the path length for theother wave decreases. For instance, when the loop is rotated in a CWdirection, the CW-traveling pump wave will have a longer optical patharound the loop than the CCW-traveling pump wave. This difference inoptical path length causes the resonant frequency for each wave todownshift or upshift accordingly.

In a typical BFOG, the cavity length of the resonator is adjustedthrough an asymmetrical feedback system so that one of the resonantmodes, for example, the resonant mode of the CW pump, coincides with thepump frequency. Thus, when the gyro is not rotating, the resonant modeof the CCW pump light equals the resonant mode of the CW pump light.However, once the gyro rotates, the resonant modes seen by the CW pumplight and CCW pump light separate, and the CCW pump light is no longerresonant. This results in a lower CCW pump intensity and accordingly, alower CW Brillouin intensity. Thus, the imbalance of the Brillouinintensity is a function of rotation rate, and the higher the rotationrate, the larger the imbalance resulting in non-linear scale factor.

The "resonant walk-off effect" also restricts the dynamic range of thegyro rotation rate. As the rotation rate of the gyro increases, the CCWpump intensity decreases to eventually become too low to sustain a CWBrillouin wave. When this happens, the beat signal disappears, and therotation rate of the gyro cannot be measured.

There are multiple thresholds for different orders of Brillouin lasingin a BFOG. When the pump intensity reaches the first threshold forstimulated Brillouin scattering, the circulating pump power within theresonant cavity is pinned. Any additional pump input power above thispinned level is built up as the first-order Brillouin circulating power.When the first-order Brillouin circulating power reaches the same levelas the circulating pump power, which is also the threshold for thesecond-order Brillouin scattering, the second-order Brillouincirculating wave is generated. The operating window between the firstBrillouin threshold and the second Brillouin threshold is referred to asthe first operating window of the BFOG.

When the gyroscope is operating at the maximum limit of the firstwindow, i.e., when the input pump power is just below the second-orderBrillouin threshold, and when asymmetrical stabilization is employed,the maximum allowed separation of resonator mode frequencies seen by theCW and CCW pump waves in present BFOG technology is ±[(√3) (Δf_(c) /2)],where Δf_(c) is the full width at half maximum of the pump cavityresonance. This occurs where the CW pump is stabilized at resonant peakand when the corresponding CCW pump is operating at 0.25 of the CW pumpintensity--the minimum to sustain a Brillouin wave.

Since the operating or dynamic range of a BFOG's rotation rate islimited by the "resonant walk off effect," it is desirable to be able toincrease the dynamic range of the rotation rate of present BFOGs.

The foregoing problems have been solved, at least in part, by inventionsdescribed in U.S. Pat. No. 5,351,252, issued on Sep. 27, 1994, forTECHNIQUE OF REDUCING THE KERR EFFECT AND EXTENDING THE DYNAMIC RANGE INA BRILLOUIN FIBER OPTIC GYROSCOPE assigned to the assignee of thepresent application. The copending application is incorporated byreference herein.

SUMMARY OF THE INVENTION

One aspect of the present invention is an apparatus for reducing theoptical Kerr effect in a Brillouin fiber optic gyroscope which has anoptical loop and a pump source that introduces counterpropagating pumplight waves into the loop. The counterpropagating pump light wavesprovide counterpropagating Brillouin light waves in the loop. Each ofthe counterpropagating Brillouin light waves provides a cross-Kerreffect on the other counterpropagating Brillouin light waves. Thecross-Kerr effect is twice a self-Kerr effect which causes anon-reciprocal Kerr effect. The present apparatus reduces or eliminatesthe non-reciprocal Kerr effect. The apparatus comprises an intensitymodulator which modulates the counterpropagating Brillouin light wavesin the loop at a substantially 50-percent duty cycle so that each of thecounterpropagating light waves experiences one-half the cross-effectfrom the other of the counterpropagating light waves. The apparatusfurther comprises a modulator that modulates the pump light waves with awaveform selected to cause the pump light waves to have frequencycomponents at predetermined intensities. The predetermined intensitiesare selected such that the Brillouin light generated by the frequencycomponents of the pump light have intensities of the correct magnitudesto generate the counterpropagating Brillouin light waves.

Another aspect of the present invention is a method for reducing theKerr effect in a Brillouin fiber optic gyroscope. The method comprisesthe step of pumping the Brillouin fiber optic gyroscope with pump lightfrom a pump source which generates light at a predetermined pumpfrequency. The method further comprises the step of modulating the pumplight with a first predetermined waveform to generate components of thepump light at sideband pump frequencies with respect to thepredetermined pump frequency. The waveform is selected to provide apredetermined relationship between magnitudes of intensities of the pumplight at each of the predetermined pump frequency and the sideband pumpfrequencies. The pump light at the predetermined pump frequency and atside sideband pump frequencies generates Brillouin light havingBrillouin components at a first Brillouin frequency and at sidebandBrillouin frequencies. The Brillouin components have magnitudes ofintensities related to the predetermined pump frequency and the sidebandpump frequencies such that the Brillouin components form periodiccounterpropagating Brillouin light waves having a second predeterminedwaveform different from the first predetermined waveform. Preferably,the periodic counterpropagating Brillouin light waves comprise squarewaves. Also preferably, the magnitudes of intensities of thepredetermined pump frequency and the sideband pump frequencies arerelated to the magnitudes of intensities of the Brillouin componentsthrough a non-linear transfer function.

The method in accordance with this aspect of the present inventionpreferably further includes the step of intensity modulating thecounterpropagating Brillouin light waves with a modulation functionselected to form the Brillouin components into the periodiccounterpropagating Brillouin light waves. The modulation functionpreferably comprises a square wave having substantially equalalternating periods of two different intensities. The step of intensitymodulating the Brillouin light waves provides the proper phaserelationship between the components.

Another aspect of the present invention is a Sagnac interferometer whichcomprises a loop comprising an optical fiber. A pump light source iscoupled to the loop to pump the fiber. The pump light has sufficientintensity to generate a pair of optical signals that counterpropagatethrough the loops. At least one optical modulation system is included tomodulate (i) the counterpropagating optical signals and (ii) the pumplight. The optical modulation system modulates each of thecounterpropagating optical signals with a first waveform such that theaverage value of the square of the intensity of the optical signal issubstantially equal to twice the square of the average value of theintensity of the optical signal. The optical modulation system modulatesthe pump light with a second waveform different than the first waveform.The shape of the second waveform is dependent on the shape of the firstwaveform.

Another aspect of the present invention is method for use with a Sagnacinterferometer which comprises a loop of optical fiber and a pump lightsource coupled to the loop to pump the optical fiber with sufficientintensity to generate a pair of counterpropagating waves in the loop.The method comprises the step of modulating the pair counterpropagatinglight waves with a first waveform having a Fourier content whichprovides plural sidebands of an optical frequency of the pair ofcounterpropagating light waves. The method comprises the further step ofmodulating the pump light with a second waveform having a Fouriercontent which causes the pump light to pump the optical fiber withfrequencies which generate optical frequencies at the plural sidebands.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a Brillouin fiber optic gyroscope (BFOG) into whichthe present invention is incorporated.

FIG. 2 illustrates a configuration of a BFOG having a feedback systemfor active power control.

FIG. 3 is a graph of circulating pump power and Brillouin power versuspump input power in a resonant optical fiber loop.

FIG. 4a depicts a BFOG configured for resonant peak stabilizationthrough extracavity coupling and phase modulation at the laser source.

FIG. 4b depicts a BFOG configured for resonant peak stabilizationthrough intracavity coupling and phase modulation at the laser source.

FIG. 5a depicts a BFOG configured for resonant peak stabilizationthrough extracavity coupling and phase modulation within the resonantcavity.

FIG. 5b depicts a BFOG configured for resonant peak stabilizationthrough intracavity coupling and phase modulation within the resonantcavity.

FIG. 6a is a response curve illustrating the relationship between thesignal corresponding to the tapped intensity obtained from extracavitycoupling, and resonator length.

FIG. 6b is a response curve illustrating the relationship between thesignal corresponding to the tapped intensity obtained from intracavitycoupling, and resonator length.

FIG. 7a illustrates the carrier signal and two sidebands obtained uponphase modulation at f_(m) at the laser source when the pump intensitiesare at resonance.

FIG. 7b1 is a graph of the carrier signal of FIG. 7a and the sideband atfrequency f_(o) +f_(m), and FIG. 7b2 is a graph of the carrier signal ofFIG. 7a and the sideband at frequency f_(o) -f_(m).

FIG. 7c1 illustrates the combination of the carrier signal of FIG. 7aand the sideband at frequency f_(o) +f_(m), and FIG. 7c2 illustrates thecombination of the carrier signal of FIG. 7a and the sideband atfrequency f_(o) -f_(m).

FIG. 7d illustrates the carrier signal and the two sidebands of FIG. 7awhen the BFOG is detuned from resonance.

FIGS. 7e1 and 7e2 illustrate the graphs of FIGS. 7b1 and 7c2 when theBFOG is detuned from resonance.

FIGS. 7f1 and 7f2 illustrate the graphs of FIGS. 7c1 and 7c2 when theBFOG is detuned from resonance.

FIG. 7g illustrates the combination of the graphs of FIGS. 7f1 and 7f2.

FIG. 7h illustrates an error signal obtained from combining the graphsof FIGS. 7f1 and 7f2.

FIG. 8a illustrates the biasing modulation scheme and the resultantmodulated signal when the resonant cavity is at rest.

FIG. 8b illustrates the biasing modulation scheme and the resultantmodulated signal when the resonant cavity is detuned from resonance.

FIG. 9a illustrates the response curves of the counterpropagating pumpsignals with respect to resonator length within a rotating resonantcavity.

FIG. 9b illustrates the error signal generated to stabilize the resonantcavity at the resonant peak of one of the counterpropagating pumpsignals as shown in FIG. 9a.

FIG. 10a illustrates an embodiment of a BFOG having a symmetric feedbacksystem for midpoint stabilization through intracavity coupling and phasemodulation at the laser source.

FIG. 10b illustrates another embodiment of a BFOG having a symmetricfeedback system for midpoint stabilization through intracavity couplingand phase modulation at the laser source.

FIG. 10c illustrates an embodiment of a BFOG having a symmetric feedbacksystem for midpoint stabilization through extracavity coupling and phasemodulation at the laser source.

FIG. 11a illustrates the response curves of counterpropagating pumpsignals with respect to resonator length and a vector illustrating themidpoint stabilization scheme for the configurations shown in FIGS. 10band 10c.

FIG. 11b illustrates the error signals corresponding to stabilization ateach resonant peak for the two counterpropagating pump signals, and thesignal obtained from the combination of these two error signals.

FIG. 11c illustrates the combination of the two error signals shown inFIG. 11b.

FIG. 12a illustrates an embodiment of a BFOG having a symmetric feedbacksystem for midpoint stabilization through extracavity coupling and phasemodulation within the resonant cavity.

FIG. 12b illustrates an embodiment of a BFOG having a symmetric feedbacksystem for midpoint stabilization through intracavity coupling and phasemodulation within the resonant cavity.

FIG. 13 illustrates an embodiment of a BFOG that incorporates bothactive power control and midpoint stabilization.

FIG. 14a illustrates the "walk-off" effect on the dynamic range ofgyroscope rotation rate for BFOGs stabilized at the resonant peak of oneof the counterpropagating signals.

FIG. 14b illustrates the increased maximum separation in the dynamicrange of FIG. 14a of a BFOG having midpoint stabilization.

FIG. 15 schematically illustrates the operation of an embodiment of aBrillouin fiber optic gyroscope in accordance with the present inventionhaving square wave intensity modulation of the two counterpropagatinglight waves.

FIGS. 16aand 16b illustrate the interaction between the twocounterpropagating light waves of FIG. 15.

FIG. 17 illustrates a graph of the spectrum of an exemplary BFOG pumpedby pump light at a plurality of pump light frequencies showing theoffset between the pump light and the Brillouin light and showing theoffset between the pump frequencies and between the Brillouinfrequencies of N×FSR.

FIG. 18 illustrates the relationship between the number of Brillouinpulses in the loop, the loop transit time and the free spectral range(FSR).

FIGS. 19a and 19b illustrate the spectrum of the Brillouin square wavesof FIG. 18 in harmonic amplitudes (FIG. 19a) and light intensities (FIG.19b).

FIG. 20 is similar to FIG. 3 and illustrates the relationship betweenthe Brillouin light intensity and the pump power intensity.

FIG. 21 shows the amplitudes of the pump power frequency componentsrequired to support the Brillouin frequency components needed togenerate square waves in the two counterpropagating Brillouin lightwaves.

FIG. 22 illustrates a preferred embodiment of a BFOG 600 constructed inaccordance with the present invention showing the modulation applied tothe pump light to generate the proper Brillouin frequencies.

FIG. 23 illustrates an embodiment of the pump light modulation waveformgenerator utilizing a PROM to generate the modulation waveform.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The theory of operation of a basic Brillouin Fiber Optic Gyroscope(BFOG) will first be presented, followed by a description of thephysical structure and operation of BFOG embodiments having midpointstabilization, followed by the embodiments of the present invention.

Theory of Operation

The Brillouin laser of the present invention utilizes a fiber opticresonator, described and claimed in U.S. Pat. No. 4,389,090, entitled"Fiber Optic Resonator", and operates as a Brillouin ring laser, asdescribed in U.S. Pat. No. 4,530,097, entitled "Brillouin Ring Laser."Both patents are assigned to the assignee of the present invention, andboth patents are incorporated herein by reference.

As shown in FIG. 1, the BFOG comprises a first strand 10 of single modeoptical fiber having a fiber arm portion 121 and a fiber arm portion161. The BFOG further includes a second strand 14 of single mode opticalfiber that forms a loop 14. The fiber arms 121 and 161 of the firstfiber 10 are coupled to the loop 14 by a fiber optic, four-portdirectional coupler 20 having ports 1 and 2 on one side thereof, andhaving ports 3 and 4 on the other side thereof. The coupler 20 has acoupling coefficient of a few percent (for example, three percent). Thefiber arm 121 of the first fiber 10 is coupled to the port 1 of thecoupler 20, and the fiber arm 161 is coupled to the port 3 of thecoupler 20. The second fiber 14 extends through the coupler 20 via theports 2 and 4 to form a complete loop.

With reference to FIG. 1, light introduced from a laser source 22 intothe input end portion 12 propagates to the port 1 of the coupler 20through the fiber arm 121, where a portion of the light (e.g., a fewpercent) is coupled to the port 4, with the remaining portionpropagating to the port 3. The light at the port 3 propagates throughthe fiber arm 161 and out the end of the fiber 10. However, the light atthe port 4 traverses the fiber loop 14 and again enters the coupler 20at the port 2, where a portion is coupled to the port 3 while theremaining propagates to the port 4, and thus propagates back into thefiber loop 14 for recirculation therein.

As described in more detail in U.S. Pat. No. 4,530,097, the loop 14 andthe coupler 20 cooperate to provide a resonant cavity so that lightentering the coupler 20 at the port 2 interferes with incoming lightfrom the laser source 22. Such interference is constructive at the port4, while being destructive at the port 3, thereby causing pump light tobuild up in the resonant cavity loop 14, provided the length of theresonator is properly adjusted.

The fiber portions 12, 16, are passed through a fiber optic, directionalcoupler 114. The coupler 114 is identical to the coupler 20, except thatits coupling constant is set at 0.5 so that approximately 50% of thelight propagating through one of the fibers 12, 16 will be coupled tothe other of the fiber arms 121,161, and vice-versa. The laser source 22is optically coupled to introduce light into the input end portion 12,while a detector 118 is optically coupled to receive light from the endof the output end portion 16. Optionally, a Y-branch beam splitter, notshown, could be used to split and recombine the light in place of thecoupler 114.

As the pump light is introduced into the input end portion 12 from thelaser source 22, it is divided into two substantially equal portions sothat approximately one-half of the pump power is in each of the fiberarm 121 and the fiber arm 161 when the light reaches the coupler 20. Atthe coupler 20, pump light from the fiber arm 161 is coupled into thefiber loop 14 from the port 3 to the port 2, and light from the fiberarm 121 is coupled to the fiber loop 14 from the port 1 to the port 4,to provide two counterpropagating pump light waves. A first pump lightwave P1 propagates in a clockwise (CW) direction in the fiber loop 14,and a second pump light wave P2 propagates in a counterclockwise (CCW)direction in the fiber loop 14.

The loop 14 is constructed to have a length selected to form a resonantcavity at the pump frequency so that the pump light waves P1 and P2 willeach build up to a maximum circulating power. Assuming the circulatingpump power is above the threshold level for Brillouin oscillation, aportion of the pump energy of each of the waves P1, P2 will be convertedinto counter-propagating Brillouin waves B1 and B2. Thus, the wave B1propagates in a direction opposite that of the wave P1 (i.e., in the CCWdirection in FIG. 1), and the wave B2 propagates in a direction oppositeto that of the wave P2 (i.e., in the CW direction in FIG. 1).

At full resonance, the circulating pump light at the ports 2 and 4interferes with incoming pump light at the ports 1 and 3, respectively,so that virtually all of the pump light remains in the loop 14, and thepump light output at the ports 1 and 3 is substantially zero. Incontrast, the stimulated Brillouin waves B1 and B2 do not interferesignificantly with the incoming pump light (because it is at a differentfrequency from the pump light), and thus, a small fraction of Brillouinlight will exit the coupler 20 as it passes therethrough. For example, afractional portion of the Brillouin wave B1 couples from the port 2 tothe port 3 for propagation through the fiber arm 161, while a fractionalportion of the Brillouin wave B2 couples from the port 4 to the port 1for propagation through the fiber arm 121. These fractional portions ofthe waves B1, B2 are combined by the coupler 114 into a Brillouin outputwave B_(out) for propagation to the detector 118 via the output endportion 16.

The detector 118 outputs a current I_(DET) on the line 120, which isproportional to the intensity of light impinging thereon. Thus, thedetector current I_(DET) will be proportional to the intensity ofI_(B).sbsb.out of the Brillouin output wave B_(OUT). The detectedintensity of the Brillouin output wave may be expressed as: ##EQU1##where I_(B1) is the intensity of the output portion of the Brillouinwave B1, I_(B2) is the intensity of the output portion of the wave B2,f_(B1) is the frequency of the wave B₁, f_(B2) is the frequency of thewave B2, and f_(B1) -f_(B2) is the beat-frequency of the output waveB_(OUT).

At zero rotation rate the frequencies of the two Brillouin waves are thesame, so that the interference term (i.e., the cosine term) in Equation(1) is one, and thus the Brillouin wave intensity I_(B) is a steadystate value however, upon rotation of the loop 14 (e.g., in acounterclockwise (CCW) direction), as indicated by the arrow 122, thecounterclockwise propagating Brillouin wave B1 will have a longeroptical path around the loop 14 than the clockwise propagating Brillouinwave B2 due to the Sagnac effect. This change in optical path lengthcauses the resonant frequency for stimulated Brillouin oscillation tochange for each direction of propagation around the loop. Accordingly,the wave B1 will resonate at a downshifted frequency, and the wave B2will resonate at an upshifted frequency, thereby yielding a frequencydifference therebetween. When the waves are combined to form the outputBrillouin wave B_(OUT), the frequency difference causes the Brillouinintensity to periodically vary as a function of the cosine of thefrequency difference (i.e., the beat-frequency), as may be seen fromEquation (1). Conventional detection electronics (not shown) areconnected to receive the electrical signals (i.e., I_(DET)) on the line120, and to thereby detect the frequency of these periodic variations inBrillouin intensity, e.g., by detecting zero crossings in the timedomain or by using a Fast Fourier Transform (FFT) spectrum analyzer inthe frequency domain.

The fiber arms 121, 161 also include polarization controllers 23, 24,respectively, to provide compensation for fiber birefringence in thearms 121, 161 so that circulating light at the ports 2 and 4 hassubstantially the same polarization as light from the laser source atthe ports 1 and 3. The operation of the polarization controller is alsodescribed in more detail in U.S. Pat. No. 4,530,097.

A feedback loop, comprising a coupler 130 with a coupling constant of afew percent, connected to the output fiber portion 16, taps a portion ofthe power to a photodetector 132. The photodetector 132 outputs acurrent proportional to the intensity of the tapped power. The output ofthe photodetector is connected to the input of stabilization electronics136 via a signal line 134. The output of the stabilizer electronics 136is connected via a signal line 138 to a piezoelectric (PZT) cylinder 140in the loop 14. The stabilization electronics 136 control the diameterof the PZT cylinder 140. Basically, the stabilization electronics 136outputs a signal on the line 138 to drive the PZT cylinder 140 by anamount necessary to restore resonance. This type of stabilization systemis fully disclosed in U.S. Pat. No. 4,634,282, which is assigned to theassignees of the present invention and which is incorporated herein byreference. The cylinder 140 stretches the fiber 14 in response tovoltage on the line 138 to dynamically vary the length of the fiber loop14. The stabilization electronics 136 operate to maintain the length ofthe loop 14 at resonance for the CCW pump signal in the manner describedin U.S. Pat. No. 4,634,282.

One of the predominant problems in existing BFOG technology, asdescribed above, is a result of the Kerr effect, which causes abeat-frequency offset and nonlinear response. The Kerr effect basicallycauses non-reciprocity between the two counterpropagating lightwaves inthe fiber coil, resulting in spurious rotation signals. It has beenfound that a power difference as small as 10 nanowatts causes a rotationerror which is too large for inertial navigation.

The Kerr effect is a phenomenon that occurs when the refractive index ofa fiber seen by a Brillouin signal is slightly modified by the signal'sown intensity, as well as by other light intensities circulating withinthe resonant cavity of the BFOG. As shown in FIG. 1, the waves B1 and B2are produced respectively by the counterpropagating pump waves P1 and P2inside the cavity. The refractive index for either Brillouin wave isperturbed by the presence of both Brillouin waves and both pump waves.When all waves in the cavity are in the same eigenpolarization mode, theindex perturbations δn for the two Brillouin waves are found from basicfield equations to be

    δn.sub.B1 =αn.sub.2 (P.sub.B1 2P.sub.B2 +2P.sub.P1 +2P.sub.2)/A.sub.eff                                      (2)

    δn.sub.B2 =αn.sub.2 (2P.sub.B1 +P.sub.B2 +2P.sub.P1 +2P.sub.P2)A.sub.eff

where A_(eff) is the effective fiber-core area and n₂ is thenonlinear-index coefficient. For linear, circular and ellipticalpolarizations, α=1,α=2/3 and 2/3<α<1, respectively. P_(B1), P_(B2),P_(P1) and P_(P2) denote power levels of circulating waves inside thecavity, with subscripts denoting the various waves. There, only firstorder Brillouin waves are assumed to be excited.

The Kerr effect can be described as follows. As well known in the art,the terms P_(B1) and P_(B2) in Equations (2) have self-modulationcoefficients of unity and cross-modulation coefficients of 2 for the twooppositely propagating waves B1 and B2. They are found, for example, inthe interferometric fiber gyro and the passive resonator gyro which haveno waves corresponding to the pump waves here. The terms in P_(P1) andP_(P2) behave as cross modulation terms for both Brillouin waves, andtherefore all have coefficients of 2.

From Equations (2), a power imbalance of ΔP_(B) =P_(B2) -P_(B1) betweenthe Brillouin waves causes a differential index perturbation Δn_(B)=δn_(B2) -δn_(B1) between waves B1 and B2. If f_(B1) and f_(B2) arerespectively the counterclockwise (CCW) and clockwise (CW) cavityresonant frequencies a beat-frequency bias Δf_(B) =f_(B2) -f_(B1) occursdue to Kerr effect, where ##EQU2## where η is the Kerr effectcoefficient, f_(B) is the average optical frequency of the Brillouinwaves, λ_(B) is the vacuum wavelength of the Brillouin waves, and n_(B)is the refractive index.

The Kerr effect coefficient η determines the dependence of theKerr-effect-induced bias on the power imbalance between the twoBrillouin waves inside the cavity in accordance with Equation (4).

Active Power Control

The BFOG illustrated in FIG. 2 utilizes a feedback system which monitorsthe difference between the circulating CW and CCW Brillouin intensities,and uses this difference in the form of a correction signal to controlthe CCW pump intensity through an intensity attenuator 270 coupled tofiber arm 121. The coupling constant of the coupler 114 is set slightlyless than 50% so that the CCW pump power P₂ is higher than the CW pumppower P₁ when the loss of attenuator 270 is minimum. The intensityattenuator 270 can be one of any conventional types; for example, aMach-Zehnder interferometer with a phase modulator on one arm.

As illustrated in FIG. 2, the BFOG comprises a coupler 150 with acoupling constant of less than one percent, coupled to the resonantcavity loop 14. The coupler 150 has a pair of input/output ports 5 and 8to which the loop fiber 14 is coupled, and has a pair of output ports 6and 7. The fiber portions 210, 220 are optically coupled tophotodetectors 230 and 240 respectively, which detect the optical poweror intensity of the light coupled to the ports 6 and 7. Thephotodetectors 230 and 240 output electrical signals on signal lines 232and 242, respectively, which signals are responsive to the detectedintensity of the light from the ports 6 and 7. The signal lines 232 and242 are connected to the inputs of a differential amplifier 250 whichprovides an output signal on a signal line 252 which is proportional tothe difference between the detected intensity of the light from theports 6 and 7. This correction signal from the differential amplifier250 is integrated by an integrator 260 which provides an averaged outputsignal on a signal line 262. The averaged output signal is provided asan input to an intensity attenuator 270 which is coupled to the inputend portion 12 of the optical fiber 10.

The fiber portions 210, 220 receive an amount of light proportional tothe light propagating in the fiber loop 14 in the clockwise andcounterclockwise directions, respectively. This light comprises bothpump light and Brillouin light propagating in each direction. Thecoupler 150 is tuned to provide a coupling constant of less than onepercent so that there is no significant reduction in the amount of lightrecirculating in the fiber loop 14. The differential amplifier 250provides an output signal representing the difference in intensitylevels between the combined light propagating in the counterclockwisedirection and the clockwise direction in the fiber loop 14. Theintegrator 260 acts as a low pass filter for the correction signalgenerated by the differential amplifier 250 to filter out extraneousnoise, fluctuations and random signals. As discussed below, theintensity attenuator 270 responds to the integrated correction signal toreduce the pump light introduced to the loop 14 in the counterclockwisedirection to equalize the light in the clockwise and counterclockwisedirections by providing an asymmetric feedback loop through the fiberarm 121. The polarity of the correction signal is selected so that whenthe differential amplifier detects a greater light intensity in thecounterclockwise light waves, the attenuation of the attenuator 270 isincreased to decrease the pump light through the fiber arm 121, and thusdecrease the pump power introduced into the counterclockwise propagatingpump light. Such a reduction in the counterclockwise propagating pumppower is continued until the Brillouin light generated by the twocounterpropagating pump waves are equal in magnitude and thecorresponding correction signal is zero. Thus, when the correctionsignal is maintained as zero through the feedback loop, the circulatingCW and CCW Brillouin intensities can be balanced. The circulatingintensities can be expressed as:

    P.sub.CW =P.sub.P1 +P.sub.B2

    P.sub.CCW =P.sub.P2 +P.sub.B1                              (5)

where P_(CW) is the total CW intensity, P_(P1) is the intensity of theclockwise pump light, P_(B2) is the intensity of the clockwise Brillouinlight, P_(CCW) is the total CCW intensity, P_(P2) is the intensity ofthe counterclockwise pump light, and P_(B1) is the intensity of thecounterclockwise Brillouin light.

Rearranging Equation (5), it can be shown that:

    P.sub.CW -P.sub.CCW =P.sub.B2 -P.sub.B1 +(P.sub.P1 -P.sub.P2)(6)

As illustrated in FIG. 3, when the pump intensity reaches the firstthreshold for Brillouin scattering, the circulating pump power withinthe resonant cavity is pinned. Any additional pump input power abovethis pinned circulating pump power builds up as the first-orderBrillouin circulating power. When this first-order Brillouin circulatingpower reaches the same level as the circulating pump power, which isalso the threshold for the second-order Brillouin scattering, asecond-order Brillouin circulating wave is generated. Thus, because theCW and CCW pump intensities are pinned and equal in the operating windowbetween the first Brillouin threshold and the second Brillouinthreshold, P_(P1) =P_(P2), and any difference in the input pump powercoupled from the fiber arm 121 and the fiber arm 161 results in adifference in the recirculating Brillouin power. Thus, a correctionsignal AP can be obtained as follows:

    ΔP=P.sub.CW -P.sub.CCW =P.sub.B2 -P.sub.B1 =ΔP.sub.B(7)

By maintaining the correction signal ΔP at zero, the difference betweenthe recirculating Brillouin waves is maintained at zero (i.e., P_(B2)-P_(B1) =0). Thus ΔP_(B) =0. Substituting this with Equation (3)provides Δf_(B) =0 so that there is no measured offset due todifferences in the pump power coupled into the fiber loop 14.

Thus, by controlling the intensity of the light introduced into thecounterclockwise propagating pump signal, the recirculating clockwiseand counterclockwise Brillouin intensities are balanced so that theproblems of beat-frequency offset and the corresponding non-linearresponse can reduced or controlled.

Midpoint Stabilization

Another aspect of the BFOG described herein is the midpointstabilization of the length of the cavity loop 14 for the twocounterpropagating pump signals. The midpoint stabilization techniquewill be explained below in connection with FIGS. 10a, 10b, 10c, 12a, 12band 13. However, in order to assist in understanding the invention, itis helpful to refer to FIGS. 4-9 which illustrate the technique used inresonant peak stabilization for typical BFOGs.

In order to obtain an error signal for stabilizing the resonant cavityfrequency at a selected value, a modulation and demodulation techniqueis used. Preferably, the pump light from the laser source 22 is passedthrough a phase modulator 300 to which a phase modulation signal havinga frequency of f_(m) is applied, as shown in FIGS. 4a and 4b.Alternatively, the intensity within the resonant cavity may be modulatedat the frequency f_(m), as illustrated in FIGS. 5a and 5b using a PZTcylinder 140. The phase modulator 300 advantageously comprises a PZTcylinder around which a length of the input end portion 12 of theoptical fiber 10 is wrapped. The modulation signal causes the PZTcylinder to periodically expand and contract at the modulation frequencyf_(m), thus causing the length of the input end portion 12 toperiodically vary, thereby causing a periodic change in the phase of thepump signal applied to the cavity loop 14. The phase modulator 300 hasthe effect of imposing a time-varying phase modulation onto the pumpsignal. Alternatively, the phase modulator 300 can be implemented on anintegrated optics chip using LiNbO₃ or other suitable materials, as iswell known in the art. If the laser source 22 has phase modulationcapabilities, those can also be used for phase modulating the pumpsignal.

As illustrated in FIG. 4a, the coupler 130 on the fiber arm 161 taps aportion of the light that exits from the cavity loop 14. This lightincludes both pump light from the CCW circulating pump signal P2 and theBrillouin light from the CCW circulating Brillouin signal B1. Theelectrical signal generated by the photodetector 132 is responsive tothe intensity of both light signals. A photodetector 132 outputs anelectrical signal proportional to the intensity of the light signal infiber arm 161.

Alternatively, as illustrated in FIG. 4b, the circulating intensitywithin the resonant cavity loop 14 may be tapped via a coupler 400. Inboth arrangements, the electrical signal on the line 134 is applied asone input to a lock-in amplifier 302 within the stabilizationelectronics 136. The other input to the lock-in amplifier 302 is thephase modulation signal having the frequency f_(m). The lock-inamplifier 302 operates as a synchronous demodulator and provides anoutput signal responsive to the pump signal P2 circulating in the cavityloop 14. This output signal is used as an error signal to stabilize theresonant cavity frequency to a selected value.

When the laser source is phase modulated at frequency f_(m), thespectrum of the light intensity obtained will consist of numerous sidebands. With reference to FIG. 7a, where the phase modulation index issmall, the carrier signal at frequency f_(o) with an amplitude J₀ andtwo side bands at frequency f₀ ±f_(m) with amplitude J₁ are dominant.The value of the sideband at f_(o) +f_(m) is positive and that of thesideband at f_(o) -f_(m) is negative.

The light throughput detected by the detector 132 in FIG. 4a or thecirculating light detected by the detector 132 in FIG. 4b has a spectrumsubstantially similar to that shown in FIG. 7a, except for the change ofamplitudes when the resonator is at resonance.

As shown in FIGS. 7b1 and 7b2 and FIGS. 7c1 and 7c2, upon detection by aphotodetector, the combination of the carrier signal at frequency f_(o)and the sideband at f_(o) +f_(m) results in a frequency component f_(m)in the detector current. Similarly, the combination of the carriersignal and the sideband at f_(o) -f_(m) produces a frequency componentf_(m) in the detector current. These two electrical signals are however,opposite in phase and cancel each other out when the carrier signal isoperating at resonance as shown in FIGS. 7c1 and 7c2.

When the resonator is detuned from resonance, the combination of thesignals discussed above will no longer result in a completecancellation. As shown in FIG. 7d, when the loop 14 is not at resonance,the carrier signal suffers a phase shift, the sign and magnitude ofwhich depends respectively on the direction and the magnitude ofdetuning from resonance. As shown in FIGS. 7e1 and 7e2 and FIGS. 7f1 and7f2, the combination of the beat frequency between the carrier signal,f_(o), and that represented by the sideband at f_(o) +f_(m), togetherwith the beat frequency between the carrier signal, f_(o), and thatrepresented by the sideband at f_(o) -f_(m) no longer cancels outbecause they are no longer opposite in phase. The resultant signal hasan f_(m) component, as shown in FIG. 7g. The error signal on the line138 is obtained by neasuring this f_(m) component and converting it toDC voltage by the stabilization electronics 136. The relationshipbetween this error signal and the change in the resonant cavity loop 14length corresponding to the difference between the resonant frequencyand the pump frequency is illustrated in FIG. 7h.

It can thus be observed that this error signal indicates the proximityof the tapped pump frequency to the resonant frequency of the cavity. Asshown in FIG. 4a and 4b, this error signal is used in a feedback loop toadjust the length of the resonant cavity loop 14 to a preselected value.

As discussed above, the circulating intensity within the resonant cavityloop 14 may also be modulated to provide the error signal for use in afeedback loop. For this arrangement, the intensity may be tapped outsidethe resonant cavity loop 14, as shown in FIG. 5a or within the resonantcavity loop 14, as shown in FIG. 5b.

The circuit in FIG. 5a is identical to that shown in FIG. 4a, with twoexceptions. First, the circuit in FIG. 5a does not require the use ofthe phase modulator 300 as shown in FIG. 4a. Second, the output of thestabilization electronics 136 is provided through signal line 138 as oneinput into an adder 139. The other input into the adder 139 is amodulation signal having a frequency f_(m). The output of the adder 139is then provided to a PZT cylinder 140.

When the operating point of the modulation for the arrangement in FIG.5a is centered about the resonant frequency, there are only evenharmonics of the fundamental frequency f_(m) in the detector current, asshown in FIG. 8a. When the operating point shifts from resonance, oddharmonics appear, as shown in FIG. 8b. The detector current, whichincludes components of f_(m), is detected by the photodetector. Thelock-in amplifier detects the f_(m) component and converts it to a DCvoltage, which is used as an error signal in the same manner asdescribed above.

Similarly, the circuit shown in FIG. 5b is identical to that shown inFIG. 4b, with the same exceptions listed above. First, the phasemodulator 300 of FIG. 4b is not used in the circuit in FIG. 5b. Second,the output of the stabilization electronics 136 is provided via thesignal line 138 as one input into an adder 139. The other input to theadder 139 is again a modulation signal having a frequency f_(m).

Although it is possible to modulate the circulating intensities withinthe resonant cavity for cavity stabilization purposes, it is not thepreferred method for two major reasons. First, when the circulatingintensities within the resonant cavity are modulated the response curvesillustrated in FIGS. 8a and 8b are only true if the modulation occursvery slowly. If a high frequency is applied to modulate the circulatingintensities, the corresponding response curves are no longer symmetricand cannot be applied to the feed back loop for cavity stabilization.Second, it is desirable to keep the circulating intensities within theresonant cavity intact and unperturbed due to design constraints. Inparticular, when the circulating intensities within the cavity aremodulated at a high frequency or with a large amplitude, the efficiencyof the circulating pump light decreases, leading to decreased Brillouinscattering. As a result, it is preferred to modulate the light at thelaser source 22 for cavity stabilization purposes as shown in FIGS. 4aand 4b.

Resonant peak stabilization can be accomplished as follows. As discussedabove, when the loop 14 is at rest, the two counterpropagating pumpwaves have the same resonant frequency. Once the loop 14 rotates, theresonant frequencies of the counterpropagating pump waves separate. Thisis illustrated, for example, in FIGS. 9a and 9b. FIG. 9a illustrates therelationship between the clockwise and counterclockwise propagating pumppower signals in the cavity loop 14 and the length of the loop 14. Aleftmost curve 308 in FIG. 9a represents the relationship of themagnitude of the counterclockwise propagating pump signal, P2 within theresonant cavity loop 14 and the length of the resonant cavity loop 14.As discussed above, when the cavity length is the resonant length of thepump signal, the circulating pump light and the incoming pump lightconstructively interfere to cause the pump light to build up in thecavity loop 14. Thus, as illustrated by the leftmost curve of FIG. 9a,the intensity of the pump signal in the loop 14 has its maximumintensity, as illustrated by a vector 310, because of the resonantcondition. The resonator length corresponding to this resonant conditionis known as the resonant length.

A rightmost curve 311 of FIG. 9a represents the magnitude of theclockwise propagating pump signal, P1, within the resonant cavity loop14 under rotation. The separation of the two curves is proportional tothe rotation rate. Under higher rotation rate, the clockwise propagatingpump power P1 built up in the loop 14 will be substantially less thanthe pump power at resonance, as illustrated by a shorter intensityvector 312. In typical BFOGs, one of the circulating pump powers (in thepresent case, P2) is "stabilized" or "locked" to operate at the resonantpeak value of the resonant cavity. When this occurs, the othercounterpropagating pump light (in the present case, P1) must operate ata lower pump power level, i.e., that represented by vector 312 underrotation.

Stabilization of one of the circulating pump powers at resonant peak isaccomplished as follows. FIG. 9b illustrates the error signal generatedby the lock-in amplifier 302. The lock-in amplifier 302 detects both theamplitude and the phase of the detector current I_(DET) on the line 134in FIGS. 4a, 4b, 5a and 5b such that the error signal has a non-zeropositive value when the cavity length is less than the resonant length(i.e., the resonant frequency of the cavity loop 14 is greater than thepump frequency) and such that the error signal has a non-zero negativevalue when the cavity length is greater than the resonant length.

The error signal output by the lock-in amplifier 302 is provided as aninput to an integrator 320. The error signal is processed by theintegrator 320 to filter out fluctuations, including high frequencysignals (e.g., any residual signal at the modulation frequency f_(m) andits harmonics, and any noise signals from the loop 14). The signaloutput from the integrator 320 drives the PZT cylinder 140 connected tothe cavity loop 14 to expand or contract radially, thus stretching orcontracting the fiber 14 to vary the fiber length so as to maintain theCW pump intensity at its resonant peak as shown in FIG. 9a. Inparticular, for the examples of FIGS. 4a, 4b, 5a and 5b, when the errorsignal has a negative value indicating that the length of the loop 14 isless than the resonant length, thus indicating that the loop length istoo long, the PZT cylinder 140 is contracted to cause the loop length todecrease toward the resonant length. In this way, the cavity loop 14 ismaintained at the resonant length for the CCW propagating pump signalP2. Conversely, when the error signal has a positive value indicatingthat the length of the loop 14 is shorter than the resonant length, thePZT cylinder 140 is expanded to cause the loop length to increase towardthe resonant length.

Alternatively, instead of adjusting the length of the cavity loop 14 bya PZT in FIGS. 4a, 4b, 5a, 5b, the frequency of the laser source 22 canbe controlled by the error signal if the laser source hasfrequency-tuning capabilities. This may be preferred when the control ofthe frequency of the laser source is easier than implementing a PZT inthe fiber loop 14.

The known BFOGs of FIGS. 4a, 4b, 5a and 5b are disadvantageous becausewhile the stabilization circuit 136 is adjusting the length of thecavity loop 14 to be optimal for the CCW pump signal P2, it iseffectively causing the length of the cavity loop 14 to become fartherfrom the resonant length for the CW pump signal P1. For example, assumethe cavity loop 14 is rotating in the counterclockwise direction toeffectively cause the loop length to become longer for the CCW pumpsignal P2 and to become shorter for the CW pump signal P1. Thestabilization circuits of FIGS. 4a, 4b, 5a and 5b counteract theeffective lengthening of the loop seen by the CCW pump signal P2 byshortening the cavity loop 14, as discussed above. This also has theeffect of shortening the cavity loop 14 for the CW pump signal P1, thuscausing the length of the cavity loop 14 to vary even more from theresonant length for the CW pump signal P1. This has the effect ofcausing the CW pump signal P1 to quickly "walk-off" from its resonantpeak, thus causing the intensity of the CW pump signal P1 to rapidlydecrease. Thus, the corresponding intensity of the CCW Brillouin lightB1 will decrease. This results in P_(B2) being larger than P_(B1), thusΔP_(B) ≠0 and causing rotation-induced beat frequency offset Δf_(B)according to Equation (3).

Furthermore as illustrated in FIG. 14a, with further rotation of thecavity loop 14, the intensity of the CW pump signal P1 will quicklydecrease so that it is below the Brillouin threshold, such that the CCWBrillouin signal B1 is no longer generated. The range of rotation thatthe BFOG will measure before the intensity of the CW pump signal P1 isinsufficient to support the generation of Brillouin light is referred toas the dynamic range. Further, it can be seen that as the intensity ofthe CW pump signal P1 is decreasing with respect to the intensity of theCCW pump signal P2, the intensity equalization circuit of FIG. 2 has toprovide additional attenuation of the CCW pump signal P2, whichdecreases the CW Brillouin light signal B2.

FIGS. 10a, 10b, 10c, 12a, 12b and 13 illustrate embodiments of BFOGswhich solve the problem with the previous embodiment of FIGS. 4a, 4b, 5aand 5b. The embodiment of FIG. 10a includes the laser source 22 whichprovides light to the input end portion 12 of the optical fiber 10. Theoutput end portion 16 is directed to the photodetector 118, as before.The phase modulator 300 is driven with the modulation signal at thefrequency f_(m). A coupler 400 is coupled to the cavity loop 14 andconnected to photodetectors 332 and 342. The electrical outputs of thetwo photodetectors 332 and 342 are connected to signal lines 334 and344, respectively. The signal lines 334 and 344 provide the outputs ofthe photodetectors 332 and 342 as inputs to lock-in amplifiers 361 and362 respectively. A modulation signal f_(m) is provided as another inputto the lock-in amplifiers 361, 362. The outputs of lock-in amplifiers361, 362 are then provided to integrators 371, 372 respectively. Theoutputs of the integrators 371, 372 are provided to an adder 350. Theresultant signal from the adder 350 drives a PZT cylinder 380, which iscoupled to the resonant cavity loop 14. The embodiment of FIG. 10aoperates as discussed above to control the PZT cylinder 380 and thuscontrol the length of the cavity loop 14; however, as discussed below,the length of the cavity loop 14 is not optimized for only one of thecounterpropagating pump signals. Rather, the length of the cavity loop14 is adjusted to maintain a balance between the intensities of the twopump signals. This reduces the power imbalance problem caused by thewalk-off discussed above, and thus reduces the rotation-induced beatfrequency offset.

The coupler 400 in FIG. 10a is advantageously identical to the coupler400 of FIG. 4b. The coupler 400 is selected to provide a couplingconstant of less than one percent so that only a small portion of thelight intensities in the cavity loop 14 are tapped. This prevents anysignificant reduction in the light intensities being measured.

As shown in FIG. 10a, optical signals proportional to the CW and CCWcirculating light intensities are tapped from the cavity loop 14 andcoupled to the first and second photodetectors 332 and 342 by thecoupler 400. The coupler 400 outputs two optical signals responsive tothe CW pump signal P1 and CW Brillouin signal B2 to a firstphotodetector 342 and to output an optical signal responsive to the CCWpump signal P2 and the CCW Brillouin signal B1 to a second photodetector332. The electrical signals generated by the photodetectors 332, 342 areprovided as inputs to the lock-in amplifiers 361, 362 respectively.These signals are simultaneously demodulated at frequency f_(m). Theoutputs of the lock-in amplifiers 361, 362 are then provided tointegrators 371, 372 respectively. The outputs of the integrators 371,372 provide the first and second error signals on signal lines 373 and374, respectively. In particular, the first error signal on the signalline 374 is proportional to the detuning of the resonator seen by the CWpump P1, and the second error signal on the signal line 373 isproportional to the detuning of the resonator seen by the CCW pump P2.Finally, the adder 350 sums the first error signal and the second errorsignal, and provides a combined error signal on the line 354. This canbe understood by referring to FIGS. 11a-11c.

With reference to FIG. 11a, the resonant length of the CW and CCW pumpsignals within the cavity loop 14 separate when the cavity loop 14rotates. For example, when the loop 14 rotates in the CCW direction, theCCW propagating pump light encounters a longer cavity lengthcorresponding to a lower resonant frequency such that the resonantlength of a resonant peak 500 of the CCW propagating pump light isshorter than an original cavity length 510. Similarly, the resonantlength of a resonant peak 520 of the CW pump light is longer by asimilar amount from the original length 510. As discussed above inconnection with FIG. 4a, the prior stabilization circuit operated tomaintain the cavity length at the resonant length for one of the pumpsignals (e.g., the CCW pump signal); however, this causes the other pumpsignal to operate further from its resonant peak, thus causing asubstantial imbalance in the circulating pump intensities. Theembodiment of FIG. 10a avoids this problem by operating upon errorsignals responsive to both the CW and CCW pump signals.

In the embodiment of FIG. 10a, the variations in intensities and phasesare detected by the synchronous demodulation of the lock-in amplifiers361 and 362. As illustrated in FIG. 11b, the CW pump signal whichpropagates in the direction having the shorter effective cavity lengthhas an error signal caused by the resonator length being shorter thanthe resonant length of the CW wave. The magnitude of the CW error signalis responsive to the difference between the CW resonant length and theactual resonator length. That is, the further the CW resonant length isfrom the actual resonator length, the lower the intensity of the CWcirculating pump signal is and the larger the CW error signal is. Thesign (i.e., polarity) of the CW error signal is shown as positive forthe original cavity length because the original cavity length is shorterthan the CW resonant length. On the other hand, the CCW error signal isshown as negative because the original cavity length is longer than theCCW resonant length. Again, the further the CCW resonant length is fromthe actual resonator length, the lower the CCW pump intensity is and thelarger the CCW error signal is.

Assuming the cavity length is balanced so that both the CW pump signaland the CCW pump signal are off resonance by substantially the samefrequency difference, the two error signals will have substantially thesame magnitude but opposite signs. Thus, as illustrated in FIG. 11c, thecombined error signal, caused by adding the two error signals, has amagnitude substantially equal to zero when the two resonant cavityfrequencies have substantially the same frequency difference from thepump frequency. If, however, the magnitude of one error signal isgreater than the magnitude of the other error signal, the resultingcombined error signal will have a non-zero value. For example, if the CWresonant length is further from the actual resonator length than the CCWresonant length, then the error signal will have a combined positivevalue, as indicated by going left from the zero value in FIG. 11 c. Thiscould occur through either the drift of laser source frequency or achange in the length of resonator loop 14 caused by temperaturefluctuations.

The resulting positive value is applied to the PZT cylinder 380 to causethe PZT cylinder 380 to expand. The expansion of the PZT cylinder 380increases the cavity length for the CW pump wave, thus reducing thedifference between the CW resonant length and the cavity length. On theother hand, the difference between the CCW resonant length and thecavity length becomes greater so that the two differences balance tobring the combined error signal back to a substantially zero value.Furthermore, if the rotation is in the opposite direction (i.e., CW),the roles of the CW pump signal and the CCW pump signal are reversed inFIGS. 11a-11c; however, the combined error signal still operates tomaintain the effective CW cavity length and the effective CCW cavitylength at values such that the two resonant cavity frequencies have thesame frequency difference from the pump frequency. That is, this aspectof the BFOG of FIG. 10a operates to provide midpoint stabilization ofthe resonant cavity length so that the resonant frequency of the cavityseen by the two pump signals is displaced from the frequency of the pumpsignal by a frequency difference such that both pump signals havesubstantially equal circulating pump intensities and are thus balanced,regardless of the rate and the direction of rotation. As a result boththe CW and CCW Brillouin signals receive the same gain, and thereforehave substantially the same intensities.

FIG. 10b illustrates another embodiment of the BFOG. This embodiment isidentical to that in FIG. 10a, with the exception that the electricalsignals generated by the photodetectors 332, 342 are provided as inputsto the adder 350. The output of the adder 350 is first provided to alock-in amplifier 360 and then to an integrator 370, which operate as inFIG. 10a to control the length of the cavity loop 14 in the same manner.The embodiment in FIG. 10b is advantageous in that it performs the samefunction as the embodiment in FIG. 10a, but requires fewer electricalcomponents, resulting in decreased error.

In another embodiment of this aspect of the BFOG illustrated in FIG.10c, couplers 330, 340 are coupled to the fiber arms 121,161respectively. The coupler 340 is advantageously identical to the coupler130 in FIG. 5a. The couplers 330, 340 in FIG. 10c output optical signalscoupled from the fiber arms 121,161 through photodetectors 332, 342respectively and provide these signals via signal lines 334, 344 to anadder 350. The sum output of the adder 350 is provided to a lock-inamplifier 360. The output of the lock-in amplifier 360 is identical tothe lock-in amplifiers 361,362 shown in FIG. 10a. Similarly, theintegrator 370 is identical to the integrators 371, 372 shown in FIG.10a. The output of the integrator 370 operate as before to drive the PZTcylinder 380 to control the length of the cavity loop 14. and therebyequalize the cavity loop 14 as described above for FIGS. 10a and 10b.

In another embodiment of the BFOG illustrated in FIGS. 12a and 12b,modulation is applied intracavity, instead of at the output of the lasersource 22, as shown in FIGS. 10a, 10b and 10c. The embodimentillustrated in FIG. 12a is identical to that shown in FIG. 10c, with twoexceptions. First, the phase modulator 300 shown in FIG. 10c is not usedin FIG. 12a. Second, the output of the integrator 370 in FIG. 12a isprovided as one input into an adder 375. The other input to the adder375 is a modulation signal f_(m). The output of the adder 375 is thenprovided into the PZT 380 which operates as discussed above.

The embodiment illustrated in FIG. 12b is similarly identical to theembodiment shown in FIG. 10b, with the same exceptions pertaining toFIG. 12a. The phase modulator 300 present in FIG. 10b is not used inFIG. 12b. In addition, the output of integrator 370 is again provided asone input into an adder 375. The other input of the adder 375 is again amodulation signal f_(m). The output of the adder 375 is similarlyprovided to the PZT cylinder 380, which operates as discussed above.

Although the intracavity phase modulation technique used in FIGS. 12aand 12b are feasible, they are limited in application, since themodulation signal f_(m) applied to these embodiments must be slow forthe reasons discussed earlier.

FIG. 13 illustrates a further embodiment of the BFOG in which the ActivePower Control embodiment of FIG. 2 and the Midpoint Stabilizationembodiment of FIG. 10b are combined into a single BFOG system. Althoughthe embodiments of FIGS. 2 and 10b could be readily combined, theembodiment of FIG. 13 combines the embodiments of FIGS. 2 and 10b sothat only the single coupler 400 and only one pair of photodetectors330, 340 are required to implement the two improvements. As discussedabove, the coupler 400 taps the circulating CW and CCW intensitiesrequired and provides these intensities to the circuitry tosimultaneously achieve power balance in the fiber arms 121, 161 and toprovide cavity stabilization in the cavity loop 14.

The pump intensities sampled through coupler 400 of FIG. 13 arecombined, demodulated. integrated and fed back to the resonator forerror correction in accordance with FIG. 10b. At the same time, thedifference in the sampled intensities may be monitored, integrated andfed back to the selective attenuator 270 so that any power sourceimbalance may be corrected. In addition, by tapping the circulatinglight signals only a single time, the losses associated with suchtapping are reduced.

As briefly discussed above, the described improvements increase thedynamic range of the BFOG by reducing the "resonant walk-off effect."The pump waves in a BFOG can resonate in the cavity only if the pumpfrequency falls within the resonance frequency of the cavity loop 14.Upon rotation of the loop 14 about an axis perpendicular to its plane,the resonant frequency of one of the pump waves is upshifted, and theresonant frequency of the other pump wave is downshifted.

The pump frequency is fixed by the frequency of the laser source 22.Thus, the shift in the resonant frequency caused by the loop rotationdoes not change the pump frequency; however, the intensities of therecirculating pump signals are reduced by the mismatch between the pumpfrequencies and the resonant frequency of the cavity loop 14 caused bythe Sagnac effect. Generally, prior to the improvements describedherein, the resonant cavity length was maintained at the resonantfrequency f_(p) of one of the counterpropagating pump waves.

As described earlier, the "resonant walk-off effect" restricts thedynamic range of the gyro. The pump waves in a BFOG can resonate in thecavity only if the pump frequency falls within the resonance frequencypeak. Referring to FIG. 14a, if the resonant length of the cavitycontinues to be maintained at the resonant frequency f_(p) of one ofcounterpropagating waves as in the prior embodiment of FIG. 4a, theintensity of the other counterpropagating wave at the resonant frequencywill diminish such that it is below the Brillouin threshold intensity,and the pump power in that wave will no longer be sufficient to causethe generation of Brillouin laser light. The maximum rotation rate thatcan be detected before this occurs is referred to as Ω_(max), and theseparation frequency is shown in FIG. 14a as Δf(Ω_(max)).

There are multiple thresholds for different orders of Brillouin lasingin a BFOG. When the pump intensity reaches the first threshold forBrillouin stimulated scattering, the circulating pump power within theresonant cavity is pinned. Any additional pump input power above thispinned level is built up as the first-order Brillouin circulating power.

When the first circulating Brillouin power reaches the same level as thecirculating pump power, which is also the threshold for the second orderBrillouin scattering, the second-order Brillouin circulating wave isgenerated. The operating window between the first-order Brillouinthreshold and the second-order Brillouin threshold is referred to as thefirst operating window of the BFOG.

When the gyroscope is operating at the maximum limit of the firstwindow, i.e. when the input pump power is just below the second-orderBrillouin threshold, and when asymmetrical stabilization is employed, asillustrated in FIG. 1, the maximum allowed separation of resonator modefrequencies seen by the CW and CCW traveling waves is ±[(√3) (Δf_(c)/2)], where Δf_(c) is the full width at half maximum of the resonantpeak (i.e., FWHM). This maximum allowed separation, illustrated in FIG.14a, occurs where the CW pump is stabilized at resonant peak and thecorresponding CCW pump is operating at the threshold for Brillouinscattering, which is 0.25 of the CCW pump intensity, as shown in FIG. 3.

The maximum rotation rate of the BFOG, corresponding to the frequencyrange of -[(√3) (Δf_(c) /2)] and +[(√3) (Δf_(c) /2)] is:

    Ω.sub.max =(√3/2) (Δf.sub.c /S)         (8)

where S is the scale factor. This maximum rotation rate in prior BFOGsis obtained by stabilizing one of the pump intensities at resonant peak.

In the above-described BFOGs having midpoint stabilization, the signalis locked at midpoint between the CW and CCW resonant mode peaks, asshown in FIG. 14b. By doing so, the BFOG of FIGS. 10a, 10b, 10c, 12a,12b and 13 will continue to operate until both recirculating pumpsignals are below the Brillouin threshold intensity. That is, the BFOGwill continue to operate until both recirculating pump intensities whilerotating are below one-quarter of the peak pump power that occurs whenthe BFOG is not rotating. This permits a wider separation between the CWand CCW resonant modes in sustaining the Brillouin signals. Since theresonant mode peaks have Laurentzian lineshapes, the correspondingimprovement obtained through midpoint stabilization is twice or a 100%increase in the dynamic range of existing BFOGs (FIG. 14a). Therein, byusing midpoint stabilization, the maximum rotation rate of the improvedBFOG becomes:

    Ω.sub.max =√3 (Δf.sub.c /S)             (9)

Description of Embodiment Using Square Wave Intensity Modulation toReduce Optical Kerr Effect

FIGS. 15-23 illustrate a further embodiment of a Brillouin fiber opticgyroscope (BFOG) in accordance with the present invention. The inventionof FIGS. 15-23 is compatible with the above-described solutions to theproblems caused by the Kerr effect in BFOGs. The basic principle of theinvention of FIGS. 15-23 comprises operating the BFOG with square wavemodulated intensities of the two counterpropagating Stokes waves insteadof using the constant intensity continuous waves described above. Theuse of square wave modulated intensities of the counterpropagating waveshas been demonstrated in interferometric fiber optic gyroscopes. Forexample, methods of compensating for the Kerr effect in non-Brillouingyroscopes have been described in R. A. Bergh, et al., "Compensation ofthe Optical Kerr Effect in Fiber-Optic Gyroscopes," OPTICS LETTERS, Vol.7, No. 6, pp. 282-284 (1982), and in U.S. Pat. No. 4,773,759. However,for the reasons set forth below, it was not believed that the squarewave modulation method described in these references could be used in astraightforward way with a BFOG.

As discussed above in connection with Equation 2, the indexperturbations caused by the optical Kerr effect have self-effect (i.e.,self-modulation) coefficients of unity and cross-effect (i.e.,cross-modulation) coefficients of two for the two oppositely propagatingwaves, B1 and B2. As previously discussed, the resulting Kerr error in aBFOG is a consequence of the factor of two difference between thecontribution of the self-effect and the cross-effect. As discussedabove, the difference between the self-effect and the cross-effectcauses a non-reciprocity in the Kerr effect, thus causing one of thecounterpropagating waves to be affected differentially with respect tothe other counterpropagating wave.

The self-effect and the cross-effect are cumulative as thecounterpropagating waves propagate through the optical loop. Thus, ifsquare wave intensity modulation is applied to the light propagatingthrough the loop to cause a fifty percent duty cycle in the lightintensities, the cross-effect can be reduced by fifty percent, thusreducing the cross-effect coefficient from two to one. This isillustrated schematically in FIG. 15.

It should be understood that when the square wave modulation describedbelow is applied to the counterpropagating Brillouin waves, mode-lockingwill occur. In particular the Brillouin waves generated in response tothe pump light have multiple modes which are not related, and therelative phases of the modes have different random values such that themodes are incoherent with one another. When the modes are made tointeract, the modes will all have definite relative phases such that thelaser is mode-locked. The resulting effect is that the Brillouin lasersignal will then comprise a series of well-defined short pulsesseparated in time. See, for example, Matt Young, Optics and Lasers,Third Revised Edition, Springer-Verlag, 1986, pp. 153-155, 165-166. Thismode-locking effect is used to advantage in the present invention.

In FIG. 15, a resonator 500 includes an optical fiber 504 and anintensity modulator 510. The intensity modulator 510 is configured toattenuate the intensity of the light propagating in the optical loop 500when it is activated. This may be accomplished, for example, by avariable coupler which couples a portion of the light out of the loopwhen activated. Alternatively, this may be accomplished by a MachoZehnder interferometer with a phase modulator on one arm. The magnitudesof the attenuation caused by the intensity modulator are selected so asto periodically reduce the intensity of the counterpropagating lightwaves to a magnitude just below the lasing threshold and then return theintensity to a magnitude just above the lasing threshold. This resultsin a series of pulses.

A square wave modulation signal, f_(sw), is applied to the intensitymodulator 510 to cause the intensity modulator 510 to be on for fiftypercent of the time and to be off for fifty percent of the time, thuscausing the light intensities in the loop to each have a respectivefifty percent duty cycle between a relatively high intensity (i.e., anintensity above the lasing threshold) and a relatively low intensity(i.e., an intensity square waves, I_(B).sbsb.CW, for example, see abelow the lasing threshold). This is illustrated schematically by thetwo propagating in the loop 500. It can thus be seen that the lightsquare waves I_(B).sbsb.CW and I_(B).sbsb.CCW which correspond to theintensities of the Billouin light in loop 500. It can thus be seen thatthe light wave I_(B).sbsb.CW, for example, sees a constant self-effectas it propagates around the loop in a clockwise direction. On the otherhand, the light I_(B) _(CW) sees time-vary cross-effect from thecounterpropagating light wave I_(B).sbsb.CCW as it passes throughsuccessive full intensity portions where Brillouin lasing is occurringand lower intensity portions of the counterpropagating wave whereBrillouin lasing is not occurring. Thus, it can be seen that byadjusting the higher and lower intensity portions of thecounterpropagating light waves to a substantially 50-percent duty cycle,the time-averaged cross-effect coefficient is reduced from two to one.

The foregoing is illustrated more clearly in FIGS. 16a 16b which showthe two counterpropagating sequences of light pulses wherein the higherintensity portion represents the portion where Brillouin lasing isoccurring and the lower intensity portion represents the portion whereBrillouin lasing is not occurring. The upper waveform 520 (FIG. 16a)represents the clockwise propagating light wave, and the lower waveform524 (FIG. 16b) represents the counterclockwise propagating waveform.Light in a pulse 530 of the clockwise propagating light I_(B).sbsb.CW520 will see continuous self-effect as it propagates around the loop. Onthe other hand, the light in the pulse 530 will see cross-effect formlight in a higher intensity pulse 534 in the counterclockwisepropagating waveform and then will see no cross-effect during a lowerintensity period 536 in that same waveform, followed by cross-effectduring a higher intensity pulse 538 in the counterclockwise propagatingwaveform. Similarly, the light in the counterclockwise propagatingwaveform I_(B).sbsb.CCW will see continuous self-effect from itself andwill see alternating periods of cross-effect and no cross-effect fromthe clockwise propagating waveform I_(B).sbsb.CW. When the waveforms areset to fifty percent duty cycle, this will have the effect of dividingthe cross-effect coefficient by one-half to reduce it from two to one sothat the time-averaged cross-effect coefficient is the same as theself-effect coefficient. Thus, this has the effect of eliminating orsubstantially reducing the nonreciprocal Kerr effect.

Implementation of the square wave modulation illustrated in FIGS. 15,16a and 16b would initially appear to be straight forward; however, itshould be understood that a square wave comprises a plurality offrequency components in order to obtain a true square wave. Simplyattenuating the two counterpropagating Brillouin light waves using theintensity modulator 510 would generate numerous harmonic components ofthe two counterpropagating waves, and the resulting waveform envelopewould not be the desired square wave. If a true square wave is notgenerated, then the fifty percent duty cycle would not have the desiredeffect of dividing the cross-effect coefficient by one-half. This isparticularly problematic in a resonant structure such as a Brillouinfiber optic gyroscope (BFOG) because the resonant structure will modifythe waveform. As described below, Applicants have discovered how tocause the two counterpropagating Brillouin light waves to formsubstantially true square waves envelopes.

FIG. 17 illustrates one of the basic principles upon which the presentinvention is based. FIG. 17 is a graph of the spectrum of an exemplaryBFOG pumped by pump light at a plurality of pump light frequencies. Thehorizontal axis represents frequency of the light, and the verticalarrows represent the frequency components of the pump light and theBrillouin light generated by the pump light. As illustrated, a pluralityof pump input components at frequencies . . . P_(-n), . . . P₀, P₁, P₂,P₃, P₄ . . . P_(n), . . . generate a corresponding plurality ofBrillouin light waves at frequencies . . . B_(-n), . . . B₀, B₁, B₂, B₃,B₄. . . B_(n) . . . The Brillouin light waves are separated in frequencyby N times the free spectral range (FSR) of the optical fiber loop 500,where N is an integer. That is, only those Brillouin frequencies thatresonate within the optical fiber loop 500 will be sustained in theloop. In order to generate the Brillouin waves, the pump light must beapplied to the loop with corresponding frequencies which are each offsetfrom a respective Brillouin frequency by the same amount and which areoffset from each other by N times the free spectral range.

The free spectral range (FSR) of a ring resonator of length L isdetermined by the following equation: ##EQU3## where c is the velocityof light in a vacuum, n is the refractive index of the optical fiber,and L is the length of the optical fiber.

In order for the square waves generated by the present invention toconstructively interfere so that the Brillouin light is sustained in theoptical loop 500, it is necessary for the square wave to be periodicwith respect to the resonant transit time of the light in the opticalloop 500. This is illustrated in FIG. 18, where T is the transit time ofthe light in the loop. As is well known, the transit time of the lightin the loop is determined by the length and the refractive index and thevelocity of the light as follows: ##EQU4## Thus, T is related to thefree spectral range as follows: ##EQU5##

Assuming that N pulses are required to be circulating in the loop, theneach pulse has a duration of ##EQU6## Therefore, the pulse frequency(i.e., repetition rate) equals ##EQU7## Because the waveform is aperiodic square wave, the square wave comprises a plurality of frequencycomponents separated by the pulse frequency. Thus, the frequencycomponents are separated by N×FSR. If the harmonic separation of thesquare wave is not equal to N×FSR, the pulses will destructivelyinterfere and the Brillouin light waves will not be sustained in theloop 500. In one particularly preferred embodiment of the presentinvention, the length L of the loop 500 is selected to be approximately20 meters, and the free spectral range (FSR) is approximately 10 MHz.The number of pulses N is selected so that there is no overlap ofBrillouin gain provided by the plurality of pump light waves atfrequencies P_(-n), . . . , P₋₁, P₀, P₁, . . . P_(n) n. For example, inthe preferred embodiment, N is selected to be 6-10 or more.

As is well known in the art, in order to generate a square wave, thesignal must comprise plurality of sinusoidal frequency componentsseparated by a frequency difference Δf=N×FSR. This is illustrated inFIG. 19a. The relative amplitudes of the frequency components arerelated to each other such that an envelope 550 can be represented asthe function ##EQU8## where ##EQU9## The ##EQU10## function degeneratesto an infinite series of decreasing amplitudes with alternating signs asillustrated in FIG. 19a, where A₀, the relative amplitude of thefundamental, equals 1; A₁, the relative amplitude of the first harmonic,is equal to 2/π which is equal to 0.6366; A₃, the relative amplitude ofthe third harmonic, is equal to ##EQU11## which is equal to -0.2122; A₅,the relative amplitude of the fifth harmonic, is equal to ##EQU12##which is equal to 0.1273; A₇, the relative amplitude of the seventhharmonic, is equal to ##EQU13## which is equal to 0.0909; A₉, therelative amplitude of the ninth harmonic, is equal to ##EQU14## which isequal to 0.7070; and so forth. When the electrical square wave isapplied to the circulating Brillouin light via the intensity modulator510 the modulation has the effect of generating sidebands of theBrillouin light separated in frequency by N×FSR. Thus, the spectrum ofFIG. 19 can also represent the center Brillouin frequency and thesurrounding sideband amplitudes. It should be understood that the lightintensities of the center Brillouin frequency and the surroundingsidebands are the corresponding amplitudes squared. Thus, as illustratedin FIG. 19b, for example, the relative intensity of the center frequencyequals 1, the relative intensity of the first harmonic component equals##EQU15## the relative intensity of the third harmonic component equals##EQU16## and so on.

As discussed above, simply controlling the intensity modulator so thatthe Brillouin light is above the lasing threshold for fifty percent ofthe time and below the lasing threshold for fifty percent of the timedoes not accomplish the desired goal. In particular, in order togenerate a square wave light pulse, both the frequencies and the phasesof the sinusoidal components of the light must be correct. In addition,each of the frequency components must have the desired magnitude so thatthe envelope of the frequency spectrum will have the desired ##EQU17##shape.

In order to generate Brillouin energy at each of the frequencies, it isnecessary to have a corresponding pump component at a frequencyseparated from the desired Brillouin frequency by the frequencydifference discussed above. Thus, for each of the Brillouin frequencycomponents shown in FIG. 19, a corresponding pump frequency componentmust be provided. In addition, the Brillouin frequency components musthave the correct phase relationships with respect to each other in orderto generate a square wave.

Although it might initially appear that applying a square wave pumpinput to the optical loop 500 would automatically generate a Brillouinsquare wave, such is not the case. FIG. 20 reproduces a portion of FIG.3 which illustrates the relationship between the Brillouin intensity andthe pump intensity in the optical fiber loop 504. In particular, FIG. 20represents the transfer function between the pump input power (i.e.,intensity) and the power (i.e., intensity) of the Brillouin lightgenerated in response to the pumping of the optical loop 500. Thehorizontal axis of the graph in FIG. 20 is the intensity of the pumpinput power labeled as I_(P).sbsb.IN. The vertical axis is the intensityof the circulating powers I_(B).sbsb.CIR and I_(P).sbsb.CIR.

As discussed before, the circulating power comprises the circulatingpump power, I_(P).sbsb.CIR and the circulating Brillouin powerI_(B).sbsb.CIR. When the input power, I_(P).sbsb.IN is below the firstBrillouin threshold, I_(B).sbsb.TH, the input pump power is transferredto the circulating pump power, as represented by the straight-lineportion 570 of the circulating pump power graph between 0 andI_(B).sbsb.TH. When the first Brillouin threshold is reached, thecirculating pump power is pinned, as illustrated by a horizontal graphportion 574, and the input power is transferred to the circulatingBrillouin power I_(B).sbsb.CIR as illustrated by a curved graph portion580 starting at I_(B).sbsb.TH. The input pump power is transferred tothe circulating Brillouin power until the second Brillouin threshold isreached at an input pump intensity of approximately four times the firstBrillouin threshold (i.e., 4×I_(B).sbsb.TH). Note, that the circulatingpump power and the circulating Brillouin power are both normalized to amaximum of 1.0.

Although the graph of the circulating Brillouin power I_(B).sbsb.CIR isshown as a substantially straight-line in FIG. 20, the graph has anon-linear transfer function as follows: ##EQU18## It should beunderstood that I_(B).sbsb.CIR in Equation 13 is normalized to a maximumvalue of 1. If the maximum value is a value other than 1, the right handside of Equation 13 can be multiplied by the maximum value (e.g.,I_(B).sbsb.MAX) to obtain an absolute value for the circulatingBrillouin light intensity. It can be seen from Equation 13 that theinput pump intensities do not have a linear relationship with thegenerated Brillouin intensities. For example, if the relationshipbetween a circulating Brillouin and the input pump intensity was alinear relationship in the operating window, then if the input pumpintensity was twice the Brillouin threshold (i.e., 2×I_(B).sbsb.TH),then the circulating Brillouin intensity would be normalized to 0.33.However, in accordance with the actual transfer function, thecirculating Brillouin intensity would be 0.41 (i.e., √2-1). Similarly,when the input pump intensity is at three times the Brillouin threshold,the circulating Brillouin intensity is approximately 0.73 (i.e., √3-1)versus 0.67 if it were a linear function.

Referring now to FIG. 21, it can be seen that the non-linearity andoffset of the graph in FIG. 20 precludes the use of a square wave pumpinput to generate the correct intensities for the frequency componentsof the Brillouin square wave. In order to generate the correctintensities to support a square wave, the pump intensities must beselected to satisfy Equation 13 above. In other words, the relative pumpintensities must be selected in accordance with the followingrelationship: ##EQU19## As in Equation 13, I_(B).sbsb.CIR is normalizedto a maximum intensity.

Equation 14 can be readily solved for each of the first 5 harmonics, forexample, to obtain the following values for the corresponding pumpintensities (C₀, C₁, C₃, C₅, C₇, C₉):

C₀ =4.0×I_(B).sbsb.TH

C₁ =[(2/π)² +1]² ×I_(B).sbsb.TH

C₃ =[(2/3π)² +1]² ×I_(B).sbsb.TH

C₅ =[(2/5π)² +1]² ×I_(B).sbsb.TH

C₇ =[(2/7π)² +1]² ×I_(B).sbsb.TH

C₉ =[(2/9π)² +1]² ×I_(B).sbsb.TH

It can be seen from the foregoing that the intensities of the harmonicsfollow a pattern such that the intensities of the higher harmonics canbe readily determined by continuing the foregoing calculations todetermine the multipliers of the higher intensities (i.e, the intensityof each harmonic is determined by dividing 2 by the product of theharmonic number times pi, squaring the result, adding 1, squaring thesecond result, and multiplying the squared second result timesI_(B).sbsb.TH).

By providing the correct intensities of the pump light at the variouspump frequencies, the intensities of the Brillouin light components areensured to have the right intensity relationship to support a squarewave and thus provide fifty percent duty cycle required to implement thepresent invention. The amplitudes of the pump signal components requiredto provide the correct pump intensities and thus to result in thecorrect Brillouin light intensities can be determined by taking thesquare roots of the pump intensities. Because the relative phases of thepump signal components do not affect the relative phases of theBrillouin amplitude components, the phases of the pump amplitudecomponents do not have to be determined.

FIG. 22 illustrates a preferred embodiment of a BFOG 600 constructed inaccordance with the present invention. The BFOG 600 of FIG. 22 issimilar to the BFOG of FIG. 13, and like numbers refer to likecomponents which perform similar functions as were described above inconnection with FIG. 13. Unlike the BFOG of FIG. 13, the BFOG 600 ofFIG. 22 includes an intensity modulator 610 which generally correspondsto the intensity modulator 510 of FIG. 15 and which is positioned in theoptical loop 14, as described above in connection with FIG. 15. Theintensity modulator 610 is driven by a waveform f₁ from a waveformgenerator 612. The waveform f₁ is selected as described above to drivethe intensity modulator 610 so that the Brillouin light in the loop 14is periodically attenuated. In particular, the waveform f₁ generated bythe waveform generator 612 is a square wave having a 50-percent dutycycle and having a frequency selected, as described above, so that Npulses are propagating in the loop 14 in each direction. That is, thefrequency of the waveform f₁ is selected so that the waveform f₁ =N×FSR.

The BFOG 600 of FIG. 22 further differs from the BFOG of FIG. 13 becausethe integrated power balance correction signal on the line 262 does notdrive the intensity attenuator 270 of FIG. 13. Rather, the correctionsignal is applied to a first input of a two-input summing amplifier 620.The output of the summing amplifier 620 drives an amplitude input to anintegrated electro-optic variable coupler 622 which replaces theconventional directional coupler 144 of FIG. 14. The electro-opticvariable coupler 622 is advantageously a commercially available Y-fedbalanced bridge modulator, such as, for example, a model APW YBBM-1.3available from United Technologies Photonics of East Hartford, Conn. Inoperation, the variable coupler 622 is responsive to the input signalfrom the summing amplifier 620 to change the proportions of the lightinput from the laser source 22 directed to the fiber arm portion 121 andthe fiber arm portion 161. Thus, the integrated correction signal on theline 262, acting through the summing amplifier 620, has the same effecton the relative proportions of the two pump signals as the intensityattenuator 170 of FIG. 13.

A second input to the summing amplifier 620 is connected to an output ofa waveform generator 630 via a signal line 632. The waveform generator630 is constructed in accordance with the present invention to generatea modulation signal Σf_(i) which modulates the pump output from thelaser source 22. The modulation signal Σf_(i) comprises a plurality ofodd harmonics of a signal having a fundamental frequency of f₁. Theamplitudes of each harmonic are selected as described above (i.e. thesquare roots of the intensities calculated in accordance with Equation14). The number of harmonics is selected so that the resulting pumpwaveform is sufficiently close to the desired pump waveform. Theharmonics could be generated using sine wave generators with adjustableamplitudes. In one embodiment of the present invention, the modulationsignal Σf_(i) is advantageously generated by a fast ROM or PROM 650, asillustrated in FIG. 23. The PROM 650 is programmed with amplitudesamples for one period of the fundamental frequency f₁. Duringoperation, the PROM 650 is operated at the sampling rate to output theprogrammed samples to a digital-to-analog converter 652. Thedigital-to-analog converter 652 converts the digital outputs of the PROM650 to the analog modulation signal Σf_(i) on the signal line 632 to thesumming amplifier 620. In the embodiment illustrated in FIG. 23, theaddress inputs to the PROM 650 are advantageously driven by the outputsof a counter 654 that counts up to a value equal to the number ofsamples and then resets to zero at the beginning of the next period ofthe fundamental frequency component of the modulation signal Σf_(i). Asillustrated, the counter 654 is preferably driven by a signal thatoperates at a frequency of S×f₁, and is reset by the signal f₁ so thatthe samples are output in synchronism with the signal f₁ which drivesthe intensity modulator 610. Preferably, the waveform generator 612 isconnected to the waveform generator 630 so that the two waveformgenerators operate from a common frequency source.

The variable coupler 622 further includes a phase input which is drivenby the modulation frequency f_(m) . The modulation frequency f_(m)controls the phase of the pump light directed to the fiber arm portion121 and the fiber arm portion 161. The modulation frequency f_(m) thushas a similar effect as in FIG. 13 by modulating the light propagatingin the optical loop 14.

It should be understood that the variable coupler 622 and the summingamplifier 620 could be replaced with separate components to perform themodulation functions shown in FIG. 13 and the additional modulationfunction in accordance with the present invention; however, the use of asingle modulator has been found to more economical in the preferredembodiment.

In operation, the modulation signal Σf_(i) on the signal line 632modulates the pump light from the laser source 22 via the variablecoupler 622. The modulation of the pump light causes the pump light tohave light in sideband frequencies at the pump frequencies necessary tosupport the Brillouin light at corresponding Brillouin frequenciesoffset from the pump frequencies. The amplitudes of the components ofthe modulation signal Σf_(i) are selected to generate correspondingmagnitudes for the components of the pump light, as discussed above, sothat the Brillouin light thus generated has components at the correctmagnitudes to generate square waves in the two counterpropagatingBrillouin light signals. Because the pump light pumps the optical fiberin the loop 14 and generates light by Brillouin scattering, theBrillouin light generated by the pump does not automatically form as asquare wave. In particular, the Brillouin scattering does not retain thephase of the pump light that causes the Brillouin scattering. In orderto create the square wave, the intensity modulator 610 is needed tocause the light in each of the counterpropagating Brillouin waves toresonate with the proper phase relationship. Any Brillouin light that isspontaneously generated from the pump light at a time that is not withinan active Brillouin pulse will be attenuated by the intensity modulator610. Thus, only light having the proper phase relationship for a squarewave will continue to circulate in the loop 14.

It can thus be seen that the waveform generator 630, acting through thesumming amplifier 620 and the variable modulator 622, and the intensitymodulator 610, driven by the waveform generator 612, operate together togenerate counterpropagating square waves in the Brillouin lightcirculating in the optical loop 14. As discussed above thecounterpropagating square waves cause the cross-effect to be reduced tounity to thereby suppress the non-reciprocal Kerr effect.

Although described above in connection with square wave modulation ofthe counterpropagating light waves, it is anticipated that alternativemodulation waveforms can be used. For example, as set forth in U.S. Pat.No. 4,773,759, assigned to the assignee of the present application andincorporated herein by reference, if the intensity of the periodicmodulation waveform is selected so that the average of the square of theintensity of the light is equal to twice the square of the averageintensity, then the non-reciprocal Kerr effect will be substantiallyreduced or eliminated. That is,

    <I.sub.0 (t).sup.2 >=2×<I.sub.0 (t)>.sup.2           (15)

where: I₀ (t) is the intensity of the counterpropagating light waves;and the surrounding brackets (i.e., <>) denotes the average of thefunction within the brackets. It can be seen that a square wave havingan intensity of 1 when on and 0 when off, and having a 50-percent dutycycle, satisfies this equation (i.e., <I₀ (t)² >=<1² +0² >=<1+0>=1/2;and <I₀ (t)>² =<1+0>² =1/2² =1/4).

Although this invention has been described in terms of a certainpreferred embodiment, other embodiments apparent to those of ordinaryskill in the art are also within the scope of this invention.Accordingly, the scope of the invention is intended to be limited by thefollowing appended claims.

What is claimed is:
 1. An apparatus for reducing the optical Kerr effect in a Brillouin fiber optic gyroscope having an optical loop and a pump source that introduces counterpropagating pump light waves into said loop, said counterpropagating pump light waves providing counterpropagating Brillouin light waves in said loop, each of said counterpropagating Brillouin light waves providing a cross-Kerr effect on the other counterpropagating Brillouin light waves, said cross-Kerr effect being twice a self-Kerr effect, said apparatus comprising:an intensity modulator which modulates said counterpropagating Brillouin light waves in said loop at a substantially 50-percent duty cycle so that each of said counterpropagating light waves experiences one-half the cross-effect from the other of said counterpropagating light waves; and a modulator that modulates said pump light waves with a waveform selected to cause said pump light waves to have frequency components at predetermined intensities, said predetermined intensities selected such that the Brillouin light generated by said frequency components have intensities of the correct magnitudes to generate said counterpropagating Brillouin light waves.
 2. A method for reducing the Kerr effect in a Brillouin fiber optic gyroscope, comprising the steps of:pumping said Brillouin fiber optic gyroscope with pump light from a pump source which generates light at a predetermined pump frequency; and modulating said pump light with a first predetermined waveform to generate components of said pump light at sideband pump frequencies with respect to said predetermined pump frequency, said waveform selected to provide a predetermined relationship between intensities of said pump light at each of said predetermined pump frequency and said sideband pump frequencies, said pump light at said predetermined pump frequency and at said sideband pump frequencies generating Brillouin light having Brillouin components at a first Brillouin frequency and at sideband Brillouin frequencies, said Brillouin components having intensities related to said predetermined pump frequency and said sideband pump frequencies such that said Brillouin components form periodic counterpropagating Brillouin light waves having a second predetermined waveform different from said first predetermined waveform.
 3. The method as defined in claim 2, wherein said periodic counterpropagating Brillouin light waves comprise square waves.
 4. The method as defined in claim 2, wherein said intensities of said predetermined pump frequency and said sideband pump frequencies are related to said intensities of said Brillouin components through a non-linear transfer function.
 5. The method as defined in claim 2, further including the step of intensity modulating said counterpropagating Brillouin light waves with a modulation function selected to form said Brillouin components into said periodic counterpropagating Brillouin light waves.
 6. The method as defined in claim 5, wherein said modulation function comprises a square wave having substantially equal alternating periods of a higher intensity and a lower intensity which result in circulating light above the lasing threshold and circulating light below the lasing threshold, respectively.
 7. The method as defined in claim 5, wherein said step of intensity modulating said Brillouin light waves provides the proper phase relationship between said components.
 8. A ring resonator comprising:a ring comprising an optical fiber; a pump light source coupled to said ring to pump said fiber, said pump light having sufficient intensity to generate a pair of optical signals that counterpropagate through said ring; at least one optical modulation system which modulates (i) said counterpropagating optical signals and (ii) said pump light, said optical modulation system modulating each of said counterpropagating optical signals with a first waveform such that the average value of the square of the intensity of the optical signal is substantially equal to twice the square of the average value of the intensity of the optical signal, said optical modulation system modulating the pump light with a second waveform different than said first waveform, the shape of said second waveform being dependent on the shape of said first waveform.
 9. In a ring resonator comprising a loop of optical fiber and a pump light source coupled to the loop to pump the optical fiber with pump light having sufficient intensity to generate a pair of counterpropagating waves in the loop, a method, comprising:modulating the pair of counterpropagating light waves with a first waveform having a Fourier content which provides plural sidebands of an optical frequency of the pair of counterpropagating light waves; and modulating the pump light with a second waveform having a Fourier content which causes the pump light to pump the optical fiber with frequencies that generate optical frequencies at said plural sidebands. 